I'm new to QM and trying to understand the basics of commutators. If you have two operators that commute, then it is said you can measure two observables simultaneously. However, I'm a bit confused: Assume $\hat{A}$ and $\hat{B}$ commute. If we express $|\psi\rangle$ in terms of the common eigenb...

There is something I really do not understand about quantum mechanics when we specifically solve, for example, the hydrogen atom. In every book about quantum mechanics we calculate the eigenfunctions by solving the time independent Schrödinger equation $$\hat{H} \Psi_{n}=E_{n}\Psi_{n} $$ But once...